The conventional brake cable bracket assembly usually has a bracket secured to the head tube of a bicycle and a nipple fixed on the bracket. A brake cable is guided through the nipple to thereby pull a brake. However, the brake cable easily incurs sharp friction with the nipple at a bottom periphery thereof thus causing unnecessary resistance and decreasing the braking effect. In addition, the brake cable is apt to suffer a problem of being worn out and cause danger for long term use. It is requisite to provide a new nipple which is rotatable in response to the pulling of the brake cable thus preventing the sharp friction between the brake cable and the nipple.